A-LevelMathematicsMechanics9709/52 · Oct/Nov 2017 · Q14 Marks

A particle P of mass 0.2kg is released from rest at a point O on a smooth horizontal surface. A horizontal force of magnitude te⁻ᵛ N directed away from O acts on P, where v ms⁻¹ is the velocity of P at time t s after release. Find the velocity of P when t = 2.

A particle P of mass 0.2kg is released from rest at a point O on a smooth horizontal surface. A horizontal force of magnitude te⁻ᵛ N directed away from O acts on P, where v ms⁻¹ is the velocity of P at time t s after release. Find the velocity of P when t = 2.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[M1] Uses Newton's Second Law to set up a differential equation. Allow a for dv/dt.
[M1] Separates the variables and integrates.
[A1] Substitutes t = 0, v = 0.
[A1] v(2) = ln11 = 2.4

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2017 Paper 5 Variant 2, question 1.

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